Posted by **Piggy** on Thursday, May 10, 2012 at 11:12pm.

A regular hexagon has an area of 96sqrt3. What is the length of each side of the hexagon?

- geometry -
**MathMate**, Friday, May 11, 2012 at 8:20am
The area of a polygon of n sides with an apothem of a and side c is

A=nac/2

For a hexagon,

n=6, apothem=c*sqrt(3)/2

so

Area=6*c*(sqrt(3)/2)*c/2

=3c²sqrt(3)

In the given case,

96sqrt(3) = 3c²sqrt(3)

Solve for c (length of side).

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